Hello, CarpeDiemKelly.
Thank you for using Apple Support Communities.
From reading your post, you want to know if there's a way to block apps completely and a way to get a report of what apps have been used. We'd like to help. Have you had a chance to review what Screen Time offers? Use Screen Time on your iPhone, iPad, or iPod touch
Check out the section for App Limits
"App Limits
You can set daily limits for app categories with App Limits. For example, you might want to see productivity apps while you're at work, but not social networking or games. App Limits refresh every day at midnight, and you can delete them any time".
To review a report, you can do so in the same article by going to the section, View your report and set limits. If you don't want to do this on their device directly, you can set up Family Sharing to view the report remotely:
"Use Screen Time with your family
With Family Sharing, you can share music, movies, apps, and more with family — and it now works with Screen Time. You can view reports and adjust settings for children in your family any time, right from your device.
If you're already in a family group, go to Settings > Screen Time, and tap your child's name. If you need to create an Apple ID for your child, go to Settings > [your name] > Family Sharing > Screen Time.
Or if you're new to Family Sharing, tap Set up Screen Time for Family and follow the instructions to add a child and set up your family. You can add family members any time from Family Sharing settings."
Best regards.
